The Optimal Inflation Rate with Discount Factor Heterogeneity

• Published date: 01 October 2022
• Author: ANTOINE LEPETIT
• Date: 01 October 2022
• DOI: http://doi.org/10.1111/jmcb.12901

DOI: 10.1111/jmcb.12901

ANTOINE LEPETIT

The Optimal Ination Rate with Discount Factor

Heterogeneity

I showthat adding an overlapping generations structure to the canonical New

Keynesian model can generate an optimal ination rate that is signicantly

positive. In a baseline calibration of the model, the optimal ination target

is comprised between 0.8% and 3.2% in annual terms. In this framework,

deviationsfrom long-run price stability are optimal because the r ate at which

rms discount future prot ows naturally differs from the rate at which the

planner discounts future utility ows.

JEL codes: E31, E32, E52

Keywords: optimal ination rate, ination target, stickyprices, optimal

monetary policy, discount factor heterogeneity, perpetual youth model

M     economies have

adopted ination targets of 2% per year. The European Central Bank ofciallychose

this target as early as 2003. In the United States, although the Federal Reserve had

been aiming for 2% ination since the mid-1990s, the target was not made ofcial

until 2012 (Summers, Wessel, and Murray 2018). Policymakers generally arguethat

this gure strikes a balance between the necessity to provide a hedge against the risk

of hitting the zero lower bound on nominal interest rates and the costs associated with

positive steady-state ination. In macro-economic models used for policy analysis,

these costs arise mainly from the presence of price stickiness. Taken in isolation, this

friction has been shown to imply that long-run price stability is optimal (Woodford

2003). This paper shows that this last conclusion no longer holds once the rate at

which the central bank discounts utility ows differs from the rate at which rms dis-

count prot ows, a situation which arises naturally when individuals are assumed

I thank the Editor Sanjay K. Chugh, two anonymous referees, as well as Florin Bilbiie, Edouard Challe,

Ippei Fujiwara, Francesco Furlanetto, Erwan Gautier, Jordan Roulleau-Pasdeloup,and participants in var-

ious seminars and conferences for their comments and suggestions. I also thank Shannon Luk for editorial

assistance. All remaining errors are my own. The views expressed in this paper are solely my respon-

sibility and should not be interpreted as reecting the views of the Board of Governors of the Federal

Reserve System.

A L is an Economist, Board of Governors of the Federal Reserve System, Division of

Research and Statistics (E-mail: Antoine.Lepetit@frb.gov).

Received April 29, 2019; and accepted in revised form October 16, 2020.

Journal of Money, Credit and Banking, Vol. 54, No. 7 (October 2022)

Published 2021. This article is a U.S. Government work and is in the public domain in the

USA.

1972 :MONEY,CREDIT AND BANKING

to have nite lives. In order to demonstrate that, I incorporate an overlapping gener-

ations structure, as in Blanchard’s (1985) and Yaari’s (1965) perpetual youth model,

in an otherwise standard dynamic stochastic general equilibrium model with imper-

fect price adjustment and study Ramsey-optimal monetary policy in a second-best

environment in which lump-sum taxes are not available.

In the model, a constant fraction of agents dies in every period and is replaced

by newcomers holding zero nancial wealth. Because new cohorts are born poor—

or, at least, poorer, on average, than existing cohorts—constant steady-state con-

sumption at the aggregate level is consistent with an increasing path for con-

sumption at the individual level. In turn, such an outcome implies that the real

interest rate is larger than the household discount rate,1that individuals accu-

mulate wealth over their lifetimes, and that generations differ in their consump-

tion and labor supply decisions. On the rm side, monopolistic rms use labor

as their only input in the production process and face quadratic costs of price

adjustment. This gives rise to a Phillips curve relating rms’ markups to ina-

tion and gives monetary policy some leverage over real activity. The decentralized

equilibrium is inefcient for several reasons. First, monopolistic competition intro-

duces a wedge between the marginal rate of substitution between consumption and

leisure and the marginal product of labor. Second, the distribution of consumption

and hours worked among households is suboptimal as young cohorts consume too

little compared to older ones. Through its effect on markups and the resource costs of

price adjustment, an increase in ination redistributes income and can partially cor-

rect for these inefciencies. The reduction in markups shifts labor demand and leads

to an increase in wages and hours worked. Along with the increase in the resource

costs incurred by rms, it also reduces prots and dividends. Thus, an increase in in-

ation benets young generations, who rely disproportionately on labor income, and

harms older generations, who rely mainly on capital income.

In this environment, the long-run optimal ination rate is positive as long as the

social discount rate, according to which the planner evaluates the lifetime utilities of

generations, is lower than the real interest rate, according to which rms discount

future prot ows. The logic behind this result is as follows. When prices are sticky,

the effects of ination on real outcomes are intrinsically dynamic. An increase in the

time tination rate decreases markups at time tbut increases markups before time t

to the extent that it is anticipated. Because rms discount the future, these effects are

asymmetric and average markups can be reduced by deviating from price stability.

However,when choosing a path for the ination rate, a monetary authority acting un-

der commitment weights the consequences of its choices according to their distance

in the future. When the social discount rate is equal to the private discount rate—

that is, the rate at which rms discount prot ows, which is given by the real interest

rate—this weighting effect perfectly offsets the effectof ination on average markups

1. Throughout the paper, I refer either to the discount rate or to the discount factor. Note that the two

are inversely related such that an increase in the discount rate corresponds to a decrease in the discount

factor. Moreover,unless otherwise specied, interest rates correspond to net interest rates.